Theoretical Economics, Volume 17, Number 3 ( 2022)

Theoretical Economics 17 (2022), 1075–1107

Persuasion with unknown beliefs

Svetlana Kosterina


A sender designs an information structure to persuade a receiver to take an action. The sender is ignorant about the receiver's prior, and evaluates each information structure using the receiver's prior that is the worst for the sender. I characterize the optimal information structures in this environment. I show that there exists an optimal signal with two realizations, characterize the support of the signal realization recommending approval and show that the optimal signal is a hyperbola. The lack of knowledge of the receiver's prior causes the sender to hedge her bets: the optimal signal induces the high action in more states than in the standard model, albeit with a lower probability. Increasing the sender's ignorance can hurt both the sender and the receiver.

Keywords: Bayesian persuasion, robust mechanism design

JEL classification: D8

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